Worm gearing



May 27, 1930.

N. TRBOJEVICH 1,759,968

WORM GEARING Filed May 19, 1924 s Sheets-Sheet 1 noeutoz flun Meiy 27, 1930; I Q N. TRBOJEVICH WORM GEARING' 3 Sheets-Sheet 2 I Ffiled May 19, 1924 attogmgs May 27, 1930;

N. TRBOJEIVICH 1,759,968

Filed May 19, 1924 3 Sheets-Sheet 3 Patented May 27, 1930 UNITED STATES PATENT OFFICE NIKOLA TRBoJEvIoH, 015 DETROIT, MICHIGAN, ASSIGNOR To GLEASON woRxs, or

' ROCHESTER, NEW YORK, A CORPORATION OF NEW YORK wORM GEARING Application filed May 19, 1924. Serial No. 714,445.

The invention relates to a wormdrive of a novel kind in which a novel cylindrical or spur worm gear meshes with one or more conical worms of constant lead. The new arrangement possesses some particular pract cal and theoretical advantages over the common form of worm drive (in which the drlving worm is cylindrical), among which may 'be -mentioned: (1) a more correct engage- 1o ment, (2) a possibility of employing two worms instead of one to mesh with the same gear, (3) a possibility of adjusting the backlash without changing the center d1stanc e, (4) a slight variation of center dlstance is of the system to a simple and accurate method of mass production. v I In generating the new worm gears one or two conical'hobs of constant pitch may be used. The conical hobs are. similar to the conical hobs which I first employed for generation of spiral bevel gears of the modified involute type (see my prior Patent Number 1,465,151 issued August 14, 1923,) and they are turned bored, gashed, relieved, hardened, and ground in the same manner as those previously described. The new worm drive 1s based upon a new theory of involute spur gearing which to my knowledge I was the first to discover and which underlies the methods of generating gears described in my cO-pending applications for patent Ser. No. 647,670, filed June 25, 1923, and Ser. No. 7( )1, 527, filed March 24, 1924, the first relating to a method of gear generating by means of largeconical hobs having less than one full convolution of helix, and the second to a method of employing double conical hobs with several convolutions of helix.

In the drawings: Figs. 1, 5, and 6 are geometrical diagrams explaining the theory of the new drive.

Fig. 2 is an elevation of the improved worm drive shown partly in section.

5 also permissible, and (5) the applicability Fig. 3 is a section thereof on the line 3-3 of Fig. 2.

Fig. 4 is the side view of said worm drive.

Figure 5 illustrates diagrammatically the plane development of the pitch cylinder C of the gear shown in Figure 2, this gear being designed to mesh with two conical worms;

Figure 6 is a similar plane development of a gear designed for meshing with a single conical worm.

My new theory of involute gearing according to which spur involute surfaces may generally be considered asthe envelopes of conical screws, is illustrated in Fig. l. Let G- be the central section or lamina of an involute worm or helical gear, and IV the axial section of a conical screw; The screw is so designed that it may correctly mesh with the lamina G with the sides of the screw thread lying nearest to the cone apex, and to accomplish this it has an axial rack section 9 having the same pitch or spacing p as the lamina to be generated, the same pressure angle a, and a cone angle also equal to oz. The two elements are so arranged in the plane of paper that the pitch circle 0, of the lamina G touches the pitch cone C of the screw W at the point A at which point the involute b drawn from the base circleC of the lamina is tangent to the side of the rack tooth (l and also the involute tooth-surface of the lamina (of which 6 is only a plane section) is tangent to the conical helicoid In other words, the as? sumption is that the helix angle of the lamina G is complementary to the helix angle of the worm W at A and the two tangent planes, one drawn to the gear, and the other to the screw at the point A coincide.

If that be so, it is easily proved that also the points A, A A A etc. all lying on the straight line 6 (the so called line of action), are points of mutual tangency of the involute lamina G with the conical helicoid NV, and that the common tangent planes to said two elements at those points are all equispaced andparallel to the first tangent plane passing through the pitch 'point A To prove this we must first recall a few funda-- mental properties of the involute spur gear ing. As it is well known the involutes b b 6 etc. are all equispaced and parallel,vand

also all inter-sect the line of action at 6 right angles at the points A A A etc.- In part\icular, the spacing I A A =A A;=A A,= cos n where p is thecircular pitch of the gear teeth I end and a the pressure angle. Now, the tan- I to itself with a uniform velocity along the side of thepi'tchcone C while the cone is uniformly rotated about its axis i. From thisfollows that the sides of the screw threads (1 d d being equally spaced along the side of the cone with a spacing p are also equally spaced alongthe line e,'said line being parallel to the axis f of the screw, and the spacing is equal to p cos 0:. Furthermore, the points A A A etc. lie on a'circular helix 7:. concentric" with the axis ofthe,screw. Because, according to the suppo ion, the cone angle of the screw is equal to t e pressure an gle of the gear, and the line e describes a cylinder (the base cylinder) about the axis 7 when said axis 'is'ro'tated. On the other hand,

' the points A 'A A, etc. also move with a Therefore, when the lamina G and the screw uniform velocity along the line 0, thus describing the circular helix or helixes h (de-' pending on the number of threads in the screw) relative to the conical screw W.

' W" are rotated in the timed relation, the helix 1 It will envelop the involutes b b 6 etc. and

the conical helic'oid taken as a surface will also envelop and generate the-involute helicoids or teeth of the gear. This theorem may be still further broadened as it is possible now to prove that the involute helicolds b 1);. etc. may be correctly generated even in the case when the axis 7 of the worm is not in the plane of paper-but isinclined with respect to. the axis of gear to an acute angle. In that case, however, in addition to the timed rotation. of the gear andscrew a relative feed movement, or a movement of translation must be imparted to the screw, said movement being in a directionparallel to the axis of gear, the same as i-n.-common hobbing.

Thus, I have discovered. a new bobbing meshin process by which involute spur gears having straight, helical or worm teeth may becorrectly generated without mutilation of the' tooth surfaces. Such is not the case with the spur hobs now used as there the pitch surface of the hob being cylindrical, the line of action e must necessarily lie on the surface of a cone and the helix A B A B etc. be-

the tangent planes with respect to the axis of hob, resulting in a slight mutilation of the gear tooth surfaces.

' Another advantage of the conical screw is that the sides of the screw thread facing the cone apex are very flat and approximate their .tangent planes intimately thus producing an effect similar to that when the gear is meshing with'a plane rack, that is, producing a maximum area and duration of engagement. It should be noted, however, that the engagement is correct only upon the sides of the screw thread facing the cone apex, while the opposite sides of the screw thread (lying farthest from the apex) exhibit very much the comes a conicalhelix having a variable helix angle and a variable angle of inclination of same properties as do the common spur hobs and worms. This feature is practically unim portant, however, because first, in most cases the gear is running always or predominantly in the same direction in which case the accur-' ately finished sides of the teeth (b 6 etc. Fig. 1) may be used for transmission of rotation, and second, two conical worms may be mounted upon the worm arbor, each worm only with one side of the thread, prefera lythe correct side. 7

An elevation of the improvedworm drive is shown in Fig. 2. Upon the wormarbor 11 two conical worms 12 and 13 are mounted in such a manner that their corresponding pitch lines 14 and 15 contact with the pitch circle C, of the'gear 16 at the points M and N. A

spacer 17 separates the "smaller ends of the worms 12 and 13 from each other in such a manner that the points of contact M and N will lie substantially in the middle of said worms.

Avkeyway 18 is cut over the whole length of the worm arbor holding the keys 19 and 20, the first preventing the worm 12 from turning with respect to the arbor 11 and the second serving as a driving means for the drive collar 21 adjacent to the'worm 13, and driving the latter by means of a pin 22. The vWorm 13 is therefore not directly keyed to the arbor 11, and by releasing the pin' 22, it

may be rotated about said arbor and. the

amount of back-lash or play between the worms 12 and 13, and the gear 16 thus accurately adjusted. As shown in Fig. 4, the drive collar 21 is provided with .ten "threaded "holes 23 while in the side of warm 13 only 9 holes are drilled. In addition there is an additional keyway 24 spaced at right angles from thekey 20, cut in the collar; By this arrangement the worm 13 may be keyed in 9 10 2=180 different positions relative to the gear 16. This number of possible adjustments is usually. suflicient for practical purposes and a still finer adjustmentis' obtainable by slightly varying the width of -the spacer 17. This particular method of adjusting the bearing of the worms against the gear is not necessarily essential and in fact,

the new drive would correctly operate in the spirit of this invention even if the two 'worms 12 and 13 were manufactured integral with the shaft 11.

Y Referring now again to the principle of engagement it is seen from Fig. 2 that the worm 13 engages the gear 16 in substantially the same manner as does the screw IV the lamina G in Fig. 1. The worm 12 also acts in a similar manner, because if we first look upon the worm 13 and make a metal picture of the geometrical configuration and then look at theworm 12 from behind the sheet of paper, the two images will be found to be identical. As both worms possess the same lead and hand of helix, the same cone and pressure angles, and as further they are symmetrically disposed relative to the gear. 16, it follows that the pitch points M and N are at the same distance from the axis f, and the cylinder 25 is the common base cylinder to both worms. Also said cylinder 25 is tangent to the base cylinder C of the gear at the point K. Therefore, when the arbor 11 is rotated the two rack elements of the worms 12 and 13 will move in the directions of the tan-' gents 14 and 15 drawn to the pitch circle C of the gear at the points M and N. Similarly, the line of contact M N 'will move tangentiallywith respect tothe base circle C the point of tangency being' at K. It is evident now that the pitch circle 0 of the gear willroll together without slipping with the imaginary rack pitch lines 14 and 15, and

" the base circle C will roll without slipping with the line M N, as the spacing of the teeth is equal to p in the first case, and to .10 cos a in the latter case, thus corresponding to the spacing of the two conical worms. I

Relative to the cone angle of the worms it should be noted that theoretically the cone angle of the worm should be equal to the Y pressure angle of gear. In practice, however, I have found it necessary to make the cone angle of the worm slightly less than or. This is necessary to do in order to avoid inter ference of the gear teeth with the hob when the hob is being fed into the worm gear, as otherwise certain portionsof' the gear teeth would be mutilated before the hobwas fully fed into the depth of cut. Thus if the pressure angle of the gear is 20 degrees I usually employ worms and hobs having a cone angle of only 19 degrees.

The teeth 26 of the gear in outward appearance are somewhat similar to those of hollow. However, the nature of contact is entirely different, because the lines of contact between the screw thread and the gear teeth are substantially parallel to the axis of the gear, whereas in the conventional worm drive they form an acute angle with respect to said axis. Further, the teeth, although helical, are substantially of the same thickness over the whole face of the gear while in the ordinary worm gears they have an hour glass cross section (thin in the middle.) These conditions are also diagrammatically illustrated in Figs. 5and 6, the former representing the plane development of the pitch cylinder 0 of the new gear when generated to mesh with two conical worms, and Fig. 6, showing a development capable of meshing with only one conical worm. As seen in Fig. 5 the teeth 26 are helically inclined with re spect to the pitch line .28 and are substantially of the same thickness in their entire lengths. The portions of screw threads 27 engaging the gear teeth have a circular segmental shape and contact with teeth 26 upon their fiat sides, that is, the sides of thread facing the cone apex, while the opposite or convex sides of thread do not touch the teeth 26 at all.

In Fig.6 the teeth 29 are generated with only one conical worm ,or hob. As already stated this arrangement may be used if the tapered hobs (mounted upon the hob arbor in exactlythe same relation as shown in Fig. 2) are rotated in a timed relation with the gear blank and gradually fed into the gear blank until the proper depth of teeth is reached. If it is not desired to employ two hobs, the same gear may be hobbed with only one hob. In that case the hob is first placed on one side of the arbor, say, in position occupied by the worm 12 in Fig. 2, and the teeth generated on one side after which the hob may be placed in the place of the worm 13 and the process repeated. Or otherwise, the hob may be left in its original position and the blank 16 reversed on its arbor and the teeth so completed.

The manufacture of the tapered worms also may be accomplished in many different ways. They may be milled in the well known millmachine, or hobbed in my spiral bevel gear hobber with tapered hobs, or with crown hobs of the modified involute type as de-- conical screws the threads of which form a rack of constant pitch in the axial plane section and an Archimedean spiral in their plane development arranged upon the same axis with their small ends adjacent, and a conjugate worm gear simultaneously meshing with both screws.

2.A worm drive consisting of two frustoconical screws, the threads of which form a rack of constant pitch in their axial 'plane section and an Archimedean spiral in their plane development arranged upon the same axis with their smaller ends adjacent, and a conjugate worm gear capable of simultaneously meshing with both screws when the axes of the screws and gear are disposed at right angles. 1 I

3. A worm drive consisting of a conical screw, the thread of which forms a'rack of constant pitch in the axialsection and an .Archimedean spiral 'in plane development,

and a conjugate worm gear operating at a fixed center distance, the axis ofv said screw and gear being arranged at right angles.

4. A worm drive consisting of two frustoconical screws arranged upon. the same axis with their smaller ends adjacent, and a conjugate worm, gear, the arrangement being such that one screw contacts with one side of each gear tooth once during each revolution of gear, and the other screw contacts with the opposite sides of teeth. I

5. A worm drive consisting of two frustoconical screws mounted upon a rotary arbor with their smaller ends adjacent, a conju- .gate worm gear having an axis disposed at right angles with respect to said rotary arbor and a central plane lying in-the same plane with said arbor.

6. A worm drive consisting of two frus'to conical screws mounted upon a rotary arbor with their smaller ends adjacent, a conjugate worm gear having an axis disposedat right angles with. respect to said rotary arbor and a central plane lying in the same plane wit said arbor, and means for rotatively 'an longitudinally adjusting the screws with respect to gear to eliminate backlash.

7. A worm drive consisting of a conical screw; of constant pitch and a conjugate worm at right angles, and means for adjusting the l gear operating at a fixed center distance, the

--.'axis of said. gear and screw being arranged screw along its axis until both sides of the' acent and screw threads lying nearest to their corresponding cone apexes.

9. A pair of mating gears consisting of a conical screw of constant pitch. having an axial rack section and a large radius of curvature on the side of the thread facing the cone apex, and a small radius on the side farthest from the apex, and a worm gear hav-- ing the same pitch and pressure angle as the rack section of the screw, the two elements engaging each other in such. a manner that the axis of the screw lies in thecentral plane Y of the gear and at right an les tothe axis thereof, and the pitch cone 0 the screw contacts with the pitch cylinder of the gear at a point oflset from the shortest distance connecting the two axes toward the large end.

of the worm so that upon each revolution' of the screw the gear rotates through an angle obtained by. developing the length of the lead of the conical helix upon the pitch circle of the gear.

10. A worm drive comprising a tapered worm, the teeth of which'form in axial sec-' tion a rack of constant pitch, and a conjugate worm gear meshing therewith and with helically arranged teeth.

' 11. A worm drive comprisinga pair of coaxially mounted tapered wormshaving conical pitch surfaces and a conjugate worm wheel having a c lindrical body and a plurality' of. helically arranged equi-Ispaced teeth, said worms beingso meshed with the worm wheel that their smallerends are ad'- are spaced axially from each other. v

12. A worm drive comprising a conical worm of constant pitch along astraight line generatrix of'the itch surface of the worm and worm wheel aving a cylindrical body and a plurality of helically arranged equiat on one side.

worm and a conjugate worm w eel having v provided :paced teeth, said teeth being substantially worm drivecomprisin a conical a cylindrical body and a. plurality of helically arrang' d equi-spaced teeth, said worm being so positioned relative to the worm wheel that it lies wholly on one side of a line perpendicular to the ;axes of worm and wheel. .I' i v I 14. A wormdriye comprising a conical worm and a conjugate worm wheel having.

a cylindrical body and a plurality of helically arranged'equispaced teeth which-are substantially flat on one side, said worm be-- ing so positioned relative to the gear that it lies wholly on one side of a line perpendicular to the axes of Worm and gear.

15, A worm drive comprising a conical worm of constant pitch and conjugate worm wheel havinga cylindrical body and a' plu- V rality of helically arranged eqni-spaced teeth which are substantially flat on one, side, said worm being'so positioned relative to the wheel that it lies wholly on one sideof a line per pendicular to the axes of worm and wheel;

16. A worm drive comprising a pair of coaxially mounted conical Worms and a worm wheel having a cylindrical body'and a plurality of helically arranged equi-spaced teeth which are substantially flat on both sides, said worms being so meshed with the 7 wheel that their smaller ends are adjacent and are spaced axially from each other;

17 A worm drive comprising a. pair of coaxially mounted conical worms of constant pitch and a worm wheel having a. cylindrical body and a plurality of helicaIly arranged equi-spaced teeth which aresubstantially flaton both sides, said worms being so meshed with the wheel that their smaller ends are adjacent and are spaced axially from each other.

In testimony whereof I aifix my signature. NIKOLA TRBOJEVICH. 

